Some Results on Related Fixed Point Theorems in Two $S$-Metric Spaces

Year 2024, Issue: 46, 110 - 117, 29.03.2024

Hakan Karayılan

https://doi.org/10.53570/jnt.1443624

Abstract

In this study, by considering the technique in the theorem of Bollenbacher and Hicks, we obtain some related fixed point theorems involving two mappings on two related complete $S$-metric spaces with certain conditions. As the applications of the main theorem, we then derive some new related fixed point theorems involving a pair of mappings in such spaces. We finally discuss the need for further research.

Keywords

$S$-metric space, fixed point, related fixed point, related complete $S$-metric space

References

• S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorems in $S$-metric spaces, Matematički Vesnik 64 (3) (2012) 258-266.
• S. Sedghi, I. Altun, N. Shobe, M. A. Salahshour, Some properties of $S$-metric spaces and fixed point results, Kyungpook Mathematical Journal 54 (2014) 113-122.
• S. Sedghi, N. Shobkolaei, M. Shahraki, T. Dǒsenovič, Common fixed point of four maps in S-metric spaces, Mathematical Sciences 12 (2018) 137-143.
• M. Shahraki, S. Sedghi, S. M. A. Aleomraninejad, Z. D. Mitrović, Some fixed point results on S-metric spaces, Acta Universitatis Sapientiae, Mathematica 12 (2) (2020) 347-357.
• N. Özgür, N. Taş, A new solution to the Rhodes' open problem with an application, Acta Universitatis Sapientiae, Mathematica 13 (2) (2021) 427-441.
• V. Popa, A. M. Patriciu, Ageneral common fixed point theorem for a pair of mappings in $S$-metric spaces, General Mathematics 29 (1) (2021) 31-39.
• V. Popa, A. M. Patriciu, A general fixed point theorem for mappings satisfying a cyclical contractive condition in $S$-metric spaces, Symmetry 13 (2021) 638 7 pages.
• H. Karayılan, Some results on fixed point of function in $S$-metric spaces, in: I. Zhelezarov (Ed.), International Scientific Conference, Gabrovo, 2023, Vol. II pp. 242-245.
• B. Fisher, Fixed points on two metric spaces, Glasnik Matematički 16 (36) (1981) 333--337.
• B. Fisher, Related fixed points on two metric spaces, Mathematics Seminar Notes 10 (1982) 17-26.
• B. Fisher, P. P. Murthy, Related fixed point theorems for two mappings on two metric spaces, Kyungpook Mathematical Journal 37 (2) (1997) 343-347.
• B. Fisher, D. Türkoğlu, Related fixed points for set-valued mappings on two metric spaces, International Journal of Mathematics and Mathematical Sciences 23 (3) (2000) 205-210.
• R. K. Nomdeo, N. K. Tiwari, B. Fisher, K. Taş, Related fixed point theorems on two complete and compact metric spaces, International Journal of Mathematics and Mathematical Sciences 21 (3) (1998) 559-564.
• V. Popa, A general fixed point theorem for two pairs of mappings on two metric spaces, Novi Sad Journal of Mathematics 35 (2) (2005) 79-83.
• V. Popa, M. Telci, Fixed point theorems for mappings implicit relations on two metric spaces, Mathematica Balkanica 20 (2) (2006) 143-152.
• M. Telci, Fixed points on two complete and compact metric spaces, Applied Mathematics and Mechanics 22 (5) (2001) 564-568.
• M. Telci, Some results on related fixed points, Journal Fixed Point Theory 2019 (2019) 5 13 pages.
• A. Bollenbacher, T. L. Hicks, A fixed point theorem revisited, Proceedings of the American Mathematical Society 102 (4) (1988) 898-900.
• L. L. Ćirić, Periodic and fixed point theorems in a quasi-metric space, Journal of the Australian Mathematical Society (Series A) 54 (1) (1993) 80-85.